A Formula for The Associated Buchsbaum-Rim Multiplicities of A Direct Sum of Cyclic Modules Ii

Futoshi Hayasaka

A Formula for The Associated Buchsbaum-Rim Multiplicities of A Direct Sum of Cyclic Modules Ii

Research output: Contribution to journal › Article › peer-review

Abstract

The associated Buchsbaum-Rim multiplicities of a module are a descending sequence of non-negative integers. These invariants of a module are a generalization of the classical Hilbert-Samuel multiplicity of an ideal. In this article, we compute the associated Buchsbaum-Rim multiplicity of a direct sum of cyclic modules and give a formula for the second to last positive Buchsbaum-Rim multiplicity in terms of the ordinary Buchsbaum-Rim and Hilbert-Samuel multiplicities. This is a natural generalization of a formula given by Kirby and Rees.

13H15, 13P99

Original language	English
Journal	Unknown Journal
Publication status	Published - May 6 2018

Keywords

Buchsbaum-Rim function
Buchsbaum-Rim multiplicity
Cyclic modules
Hilbert-Samuel multiplicity

ASJC Scopus subject areas

General

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N2 - The associated Buchsbaum-Rim multiplicities of a module are a descending sequence of non-negative integers. These invariants of a module are a generalization of the classical Hilbert-Samuel multiplicity of an ideal. In this article, we compute the associated Buchsbaum-Rim multiplicity of a direct sum of cyclic modules and give a formula for the second to last positive Buchsbaum-Rim multiplicity in terms of the ordinary Buchsbaum-Rim and Hilbert-Samuel multiplicities. This is a natural generalization of a formula given by Kirby and Rees.13H15, 13P99

AB - The associated Buchsbaum-Rim multiplicities of a module are a descending sequence of non-negative integers. These invariants of a module are a generalization of the classical Hilbert-Samuel multiplicity of an ideal. In this article, we compute the associated Buchsbaum-Rim multiplicity of a direct sum of cyclic modules and give a formula for the second to last positive Buchsbaum-Rim multiplicity in terms of the ordinary Buchsbaum-Rim and Hilbert-Samuel multiplicities. This is a natural generalization of a formula given by Kirby and Rees.13H15, 13P99

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KW - Buchsbaum-Rim multiplicity

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KW - Hilbert-Samuel multiplicity

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